Most of the action takes place between Sonya's birthday, which is in July, as evidenced by her birthstone, the ruby), and Yom Kippur, which is in the early fall. However, in all the outdoor scenes, it is clearly winter, as evidenced by the winter coats on all characters and extras.
After the bris (circumcision ceremony), Mendel apologizes to Sonia for naming their son Shimmie "after the Rebbe." Shimmie is a nickname for Shim'on (Simon). However, the Rebbetzin (the Rebbe's wife) calls her husband Moishe. Also, at the eulogy for the Rebbe, the speaker refers to the him as "our own Moishe Rabbenu," clearly making a connection between him (and his name) and the prophet Moses.